Sophia Explores Symmetry

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Quotes of the Day

Symmetry is also economy.
Symmetry is simplicity.”
― Alan Lightman
Gastrulation is a phase early in the embryonic development of most animals,
during which the single-layered blastula
is reorganized into a multilayered structure known as the gastrula.
Before gastrulation,
the embryo is a continuous epithelial sheet of cells;
by the end of gastrulation,
the embryo has begun differentiation to establish distinct cell lineages,
set up the basic axes of the body (e.g. dorsal-ventral, anterior-posterior),
and internalized one or more cell types including the prospective gut.
--Gastrulation, Wikipedia

Contemplation for the Day

Let us imagine

You are swimming underwater in the Ocean with your elephant. The water seems thick, syrupy and you recognize the feeling from the time you were a protozoan just learning to be multicellular. You and your elephant have been miniaturized but not down to the size of a single cell.

Off to your right you see something in the water. Curious as to what it is, your elephant leads you to it. And as you approach, you see that it is Sophia in her form of many little girls, their glowing blue eyes scanning through the water, their little arms flailing above their heads. They are indeed very little girls, miniaturized to the same degree you are. But they are gathered into a ball almost as large as your elephant. Their feet must be together toward the centre so that the surface of the sphere is formed of their shoulders, heads and arms.

One of the girls speaks, "This spherical symmetry works pretty well. We can defend ourselves from an attack equally in all directions." You notice that tiny dark ovoid creatures are swimming toward the ball. As each one approaches, a Sophia-body reaches out and grabs it with one hand and crushes it in her grip. Then she or her neighbouring bodies absorbs its remains through their skin.

Another Sophia-body, just having absorbed the remains of a tiny purple ovoid says, "And in defending ourselves, we can also feed ourselves!"

Then a jellyfish approaches. It isn't much bigger than the Sophia-ball, but it reaches out with its tentacles toward the Sophia-ball, its mouth distending in order to swallow her.

One of the Sophia-bodies yells, "Oh me goddess, look at the size of that mouth. It is going to swallow us whole. Quick, escape!"

All the Sophia's start flailing their arms frantically. The sphere spins a little but does not take off in any direction. The tentacles of the jellyfish undulate, and the jellyfish closes in on them. They flail some more and spin some more but the tentacles of the jelly fish latch on to the ball. Some of the Sophia’s wrestle with the tentacles trying to pry their stinging barbs from their skin but their tiny arms are no use against the powerful jelly fish tentacles. Each tentacle is the size of an entire Sophia-body and although the jelly fish has fewer tentacles than the ball has Sophia-Arms, each tentacle is much more powerful and soon the Sophia-Ball is drawn into the Jelly fish mouth.

Your elephant charges forward bravely and prods the jellyfish with its tusks piercing the jellyfish's skin. The jellyfish yelps in pain and spits out the Sophia-ball in order to get away from the sharp elephant tusks.

"Thank you, Just One." The Sophia-bodies say together in unison, "I was nearly consumed. That would have been embarrassing; a goddess consumed by a mere planktonic cnidarian."

"Why are you so small, Sophia?" you ask, "Why are you floating around in water?"

"Wisdom scales perfectly, Just One." The Sophia-bodies reply in their disquieting unison again, "I am trying to learn about the implications of different symmetries."

One of the Sophia-bodies is watching the jellyfish retreat, "Radial symmetry allows for directional locomotion." She separates herself from the rest of the Sophia-ball and continues, "We need an axis and this body will serve, form a radial body around me!" She stretches herself out, legs straight, feet pointed, arms straight above her head, hands together pointed straight up. She forms a straight axis.

The other Sophia bodies break up and the sphere dissolves. Each body swims over to the axis-Sophia and plants her feet at a different point along the axis so that her body stretches out at ninety degrees to the axis. Soon they have reformed into a disc, whole layers of Sophia bodies undulating together drive the Sophia-disc upward slowly. One Sophia-body cries, "Yay! Now we have directional locomotion."

A few Sophia-bodies from somewhere under the flapping layers cry, "We have organized ourselves down here into a mouth and stomach. Pass us food and we will break it down for everybody else while you all focus on catching food and moving us around."

Several Sophia-bodies climb their neighbours and get their neighbours to hold onto them by their feet so that they can reach far out into the water and grab little purple oblongs that are trying to escape. Then these double-tall Sophia-body pairs act like giant tentacles and reach under the flapping layers of Sophia-bodies to pass the little oblongs to the specialized mouth and stomach.

"Wow, this radial symmetry is great!" yells one Sophia-body and then she notices the shark. It is heading straight toward them and she calls, "Go faster, faster, that shark is going to eat us!" The layers of Sophia-bodies flap harder and the Sophia-disc slowly makes it way through the water, but the shark is propelling itself at a much higher speed. Soon it will be upon them. You can imagine row upon row of razor-sharp teeth.

Again, your elephant charges forward bravely into the path of the shark and you punch the shark in the eye; momentarily blinded and startled it turns from its prey and disappears into the murky water.

"Thank you again, Just One." Sophia says in her unison voice.

Then one of the Sophia-bodies, as she watches the shark disappear, "Bilateral symmetry allows for much greater specialization, faster locomotion and cephalization." She separates herself from the flapping mess of Sophia-bodies and says, "We need to organize ourselves into right and left halves."

The Sophia-bodies arrange in pairs, feet to feet, lined up in rows with their feet all together as if standing out sideways from the two sides of a single wall. And then some of the pairs detach from the imaginary wall and each other and swim out to form fins and a tail at one end and a great gaping mouth at the other. From every pair one member goes to the left side and the other to the same spot on the right side. And soon the Sophia-bodies have formed themselves into a shark. The tail sweeps from side to side and they move forward. You notice that some of the Sophia-bodies have even reshaped themselves into sharp shark teeth in the mouth. The Sophia-shark sweeps around in a wide curve always travelling mouth first, taking in oxygenated water through the mouth and letting go of de-oxygenated water through gills slits (really just Sophia-bodies with gaps between them).

"So many symmetries to explore and yet bilateral symmetry is so powerful it outcompetes almost all of the others in so many niches." You hear Sophia say in her unison voice as she swims out of sight.

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